Here is Fitting the t-Distribution by Maximum Likelihood t-method in book
Statistics and Data Analysis for Financial Engineering with R examples page 113 and 168.
But I cannot understand
For the univariate case (first picture):
How does the fitting work? Is it the method called
expectation–maximization (EM) algorithm?
And I understood as first we obtain $\mu,\sigma$ by fitting, then use MLE to obtain the parameter $\nu,$ is it correct?
For the multivariate case (second picture):
Does that mean we first compute $\nu,$ then use MLE to compute $\mu$ and $\Lambda?$
If so, then how could we compute $\nu$ with unknown $\mu$ and $\Lambda?$ And the logic totally reverses compared with the univariate case.
I think the parameter estimation should be consistent between univariate and multivariate cases and I must have a big misunderstanding.